Indicators of similarity and dissimilarity of multi-attribute objects in metric spaces of sets and multisets

The notions of similarity and dissimilarity (difference) of the analyzed objects play an important role in many theoretical and practical problems of decision making, artificial intelligence, pattern recognition, processing of heterogeneous information, and others. The similarity or dissimilarity of objects is usually estimated by their proximity in the attribute space. The paper considers new classes of metric spaces of the finite, bounded, measurable sets and multisets. Possibilities of using new types of metrics for evaluating the similarity or dissimilarity of multi-attribute objects that are present in several exemplars with differing values of attributes and are represented by multisets of attributes are shown.